Asymptotic Efficiency of Semiparametric Two-step GMM
研究了半参数模型中有限维参数的半参数效率界，并证明两步最优加权GMM估计量能达到该效率界，其中第一步可用任意一致的非参数方法估计冗余函数。
Many structural economics models are semiparametric ones in which the unknown nuisance functions are identified via non-parametric conditional moment restrictions with possibly non-nested or overlapping conditioning sets, and the finite dimensional parameters of interest are over-identified via unconditional moment restrictions involving the nuisance functions. In this article we characterize the semiparametric efficiency bound for this class of models. We show that semiparametric two-step optimally weighted GMM estimators achieve the efficiency bound, where the nuisance functions could be estimated via any consistent non-parametric methods in the first step. Regardless of whether the efficiency bound has a closed form expression or not, we provide easy-to-compute sieve-based optimal weight matrices that lead to asymptotically efficient two-step GMM estimators.